INSTRUCTOR’S SOLUTIONS
MANUAL
DAVID ATWOOD
Rochester Community and Technical College
TU
BEGINNING AND
INTERMEDIATE ALGEBRA
TO
WITH A PPLICATIONS AND
VISUALIZATION
R
FOURTH E DITION
Gary Rockswold
G
Terry Krieger
U
R
Jessica Rockswold
U
, Table of Contents
Chapter 1 Introduction to Algebra 1
Chapter 2 Linear Equations and Inequalities 51
TU
Chapter 3 Graphing Equations 115
Chapter 4 Systems of Linear Equations in Two Variables 199
Chapter 5 Polynomials and Exponents 253
Chapter 6 Systems of Equations and Inequalities 305
TO
Chapter 7 Rational Expressions 357
Chapter 8 Introduction to Functions 433
Chapter 9 Systems of Linear Equations 503
Chapter 10 Radical Expressions and Functions 539
R
Chapter 11 Quadratic Functions and Equations 599
Chapter 12 Exponential and Logarithmic Functions 673
G
Chapter 13 Conic Sections 729
Chapter 14 Sequences and Series 769
U
R
U
,Section 1.1: Numbers, Variables, and Expressions 1
Chapter 1: Introduction to Algebra
Section 1.1: Numbers, Variables, and Expressions
1. natural
2. 0
3. 1
4. composite
TU
5. factors
6. formula
7. variable
8. equal sign
9. sum
TO
10. product
11. quotient
12. difference
13. Yes, the population of a country could be described by the whole numbers because we cannot have a
fraction of a person.
14. No, the cost of a gallon of gas could not be described by the whole numbers because the cost of a
R
gallon of gas is not usually an even dollar amount.
15. No, a student’s grade point average could not be described by the whole numbers because a grade
point average usually contains a decimal point.
G
16. No, the Fahrenheit temperature in Antarctica could not be described by the whole numbers because a
temperature reading contains a decimal point.
17. Yes, the number of apps stored on an iPad could be described by the whole numbers because the
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number of apps does not contain a fraction or a decimal point.
18. Yes, the number of students in a class could be described by the whole numbers because we cannot
have a fraction of a person.
R
19. No, the winning time in a 100-meter sprint, could not be described by the whole numbers because the
winning time would be expressed in the number of seconds plus a fraction of an seconds.
20. Yes, the number of bald eagles living in the United States could be described by the whole numbers
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because we cannot have a fraction of an eagle.
21. The number 4 is a composite number because it has factors other than itself and 1; 4 = 2 2.
22. The number 36 is a composite number because it has factors other than itself and 1; 36 = 2 2 3 3.
23. The number 1 is neither a prime nor a composite number.
24. The number 0 is neither a prime nor a composite number.
25. The number 29 is a prime number because its only factors are itself and 1.
26. The number 13 is a prime number because its only factors are itself and 1.
Copyright ©2018 Pearson Education, Inc.
, 2 Chapter 1 Beginning and Intermediate Algebra
27. The number 92 is a composite number because it has factors other than itself and 1; 92 = 2 2 23.
28. The number 69 is a composite number because it has factors other than itself and 1; 69 = 3 23.
29. The number 225 is a composite number because it has factors other than itself and 1; 225 = 3 3 5 5.
30. The number 900 is a composite number because it has factors other than itself and 1;
900 = 2 2 3 3 5 5.
31. The number 149 is a prime number because its only factors are itself and 1.
32. The number 101 is a prime number because its only factors are itself and 1.
33. 6 = 2 3
TU
34. 8 = 2 2 2
35. 12 = 2 2 3
36. 20 = 2 2 5
37. 32 = 2 2 2 2 2
38. 100 = 2 2 5 5
TO
39. 39 = 313
40. 51 = 3 17
41. 294 = 2 3 7 7
42. 175 = 5 5 7
43. 300 = 2 2 3 5 5
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44. 455 = 5 7 13
45. The value of the expression 3x, when x = 5, is 3x = 3(5) = 15.
46. The value of the expression x +10, when x = 8, is x +10 = 8 +10 = 18.
G
47. The value of the expression 9 − x, when x = 4, is 9 − x = 9 − 4 = 5.
48. The value of the expression 13x, when x = 0, is 13x = 13(0) = 0.
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x x 32
49. The value of the expression , when x = 32, is = = 4.
8 8 8
5 5 5 5
50. The value of the expression , when x = 8, is = = = 1.
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x −3 x −3 8−3 5
51. The value of the expression 3( x +1), when x = 5, is 3( x +1) = 3(5 +1) = ( 3 )( 6 ) = 18.
52. The value of the expression 7 (6 − x ) , when x = 3, is 7 (6 − x) = 7 (6 − 3) = ( 7 )( 3 ) = 21.
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x x 6
53. The value of the expression +1, when x = 6, is +1 =
+1 = 3 +1 = 4.
2 2 2
6 6 6
54. The value of the expression 3 − , when x = 2, is 3 − = 3 − = 3 − 3 = 0.
x x 2
55. When x = 8 and y = 14, x + y = 8 +14 = 22.
56. When x = 2 and y = 3, 5xy = ( 5 )( 2 )( 3 ) = 30.
Copyright ©2018 Pearson Education, Inc.
MANUAL
DAVID ATWOOD
Rochester Community and Technical College
TU
BEGINNING AND
INTERMEDIATE ALGEBRA
TO
WITH A PPLICATIONS AND
VISUALIZATION
R
FOURTH E DITION
Gary Rockswold
G
Terry Krieger
U
R
Jessica Rockswold
U
, Table of Contents
Chapter 1 Introduction to Algebra 1
Chapter 2 Linear Equations and Inequalities 51
TU
Chapter 3 Graphing Equations 115
Chapter 4 Systems of Linear Equations in Two Variables 199
Chapter 5 Polynomials and Exponents 253
Chapter 6 Systems of Equations and Inequalities 305
TO
Chapter 7 Rational Expressions 357
Chapter 8 Introduction to Functions 433
Chapter 9 Systems of Linear Equations 503
Chapter 10 Radical Expressions and Functions 539
R
Chapter 11 Quadratic Functions and Equations 599
Chapter 12 Exponential and Logarithmic Functions 673
G
Chapter 13 Conic Sections 729
Chapter 14 Sequences and Series 769
U
R
U
,Section 1.1: Numbers, Variables, and Expressions 1
Chapter 1: Introduction to Algebra
Section 1.1: Numbers, Variables, and Expressions
1. natural
2. 0
3. 1
4. composite
TU
5. factors
6. formula
7. variable
8. equal sign
9. sum
TO
10. product
11. quotient
12. difference
13. Yes, the population of a country could be described by the whole numbers because we cannot have a
fraction of a person.
14. No, the cost of a gallon of gas could not be described by the whole numbers because the cost of a
R
gallon of gas is not usually an even dollar amount.
15. No, a student’s grade point average could not be described by the whole numbers because a grade
point average usually contains a decimal point.
G
16. No, the Fahrenheit temperature in Antarctica could not be described by the whole numbers because a
temperature reading contains a decimal point.
17. Yes, the number of apps stored on an iPad could be described by the whole numbers because the
U
number of apps does not contain a fraction or a decimal point.
18. Yes, the number of students in a class could be described by the whole numbers because we cannot
have a fraction of a person.
R
19. No, the winning time in a 100-meter sprint, could not be described by the whole numbers because the
winning time would be expressed in the number of seconds plus a fraction of an seconds.
20. Yes, the number of bald eagles living in the United States could be described by the whole numbers
U
because we cannot have a fraction of an eagle.
21. The number 4 is a composite number because it has factors other than itself and 1; 4 = 2 2.
22. The number 36 is a composite number because it has factors other than itself and 1; 36 = 2 2 3 3.
23. The number 1 is neither a prime nor a composite number.
24. The number 0 is neither a prime nor a composite number.
25. The number 29 is a prime number because its only factors are itself and 1.
26. The number 13 is a prime number because its only factors are itself and 1.
Copyright ©2018 Pearson Education, Inc.
, 2 Chapter 1 Beginning and Intermediate Algebra
27. The number 92 is a composite number because it has factors other than itself and 1; 92 = 2 2 23.
28. The number 69 is a composite number because it has factors other than itself and 1; 69 = 3 23.
29. The number 225 is a composite number because it has factors other than itself and 1; 225 = 3 3 5 5.
30. The number 900 is a composite number because it has factors other than itself and 1;
900 = 2 2 3 3 5 5.
31. The number 149 is a prime number because its only factors are itself and 1.
32. The number 101 is a prime number because its only factors are itself and 1.
33. 6 = 2 3
TU
34. 8 = 2 2 2
35. 12 = 2 2 3
36. 20 = 2 2 5
37. 32 = 2 2 2 2 2
38. 100 = 2 2 5 5
TO
39. 39 = 313
40. 51 = 3 17
41. 294 = 2 3 7 7
42. 175 = 5 5 7
43. 300 = 2 2 3 5 5
R
44. 455 = 5 7 13
45. The value of the expression 3x, when x = 5, is 3x = 3(5) = 15.
46. The value of the expression x +10, when x = 8, is x +10 = 8 +10 = 18.
G
47. The value of the expression 9 − x, when x = 4, is 9 − x = 9 − 4 = 5.
48. The value of the expression 13x, when x = 0, is 13x = 13(0) = 0.
U
x x 32
49. The value of the expression , when x = 32, is = = 4.
8 8 8
5 5 5 5
50. The value of the expression , when x = 8, is = = = 1.
R
x −3 x −3 8−3 5
51. The value of the expression 3( x +1), when x = 5, is 3( x +1) = 3(5 +1) = ( 3 )( 6 ) = 18.
52. The value of the expression 7 (6 − x ) , when x = 3, is 7 (6 − x) = 7 (6 − 3) = ( 7 )( 3 ) = 21.
U
x x 6
53. The value of the expression +1, when x = 6, is +1 =
+1 = 3 +1 = 4.
2 2 2
6 6 6
54. The value of the expression 3 − , when x = 2, is 3 − = 3 − = 3 − 3 = 0.
x x 2
55. When x = 8 and y = 14, x + y = 8 +14 = 22.
56. When x = 2 and y = 3, 5xy = ( 5 )( 2 )( 3 ) = 30.
Copyright ©2018 Pearson Education, Inc.
